This eigendecomposition is connected to the Koopman operator
of the system, and allows reconstructions and predictions [1]}, [2]}, [3]}, [4]}.
For example, for a discrete-time system (i.e., \(y_k = x_{k+1}\) ) with evenly spaced samples in time, then the eigenvectors form a linearly independent set and
\(x_j = \Psi \Lambda ^{j-1} b\) 
